 # 6.11 Patterns with multiplication

Lesson

## Ideas

Do you remember how to use  repeated addition  to solve multiplication?

### Examples

#### Example 1

Write this addition as a multiplication.

4+4+4+4

Worked Solution
Create a strategy

Rewrite the addition as a multiplication in this form:

Number of groups \times amount in each group

Apply the idea

We are adding 4 groups of 4.

4+4+4+4= 4 \times 4

## Patterns with multiplication

When we need to multiply, it can help to see if there are any patterns that help us. Let's look at some in this video.

### Examples

#### Example 2

Complete the following pattern.

Start at 8 and double the answer each time.

8, \,⬚, \, ⬚, \, ⬚

Worked Solution
Create a strategy

Doubling is the same as multiplying by 2.

Apply the idea

To multiply 16 by 2 we can use a vertical algorithm:

\begin{array}{c} & &1 &6 \\ &\times && 2 \\ \hline \\ \hline \end{array}

First we multiply 2 by 6 which is 12. So we put 2 in the units column and carry the 1:\begin{array}{c} & & {}^1 1 &6 \\ &\times && 2 \\ \hline &&&2 \\ \hline \end{array}

Multiply 2 by 1 and add the carried 1 to get 3. We put this in the tens column:\begin{array}{c} & & {}^1 1 &6 \\ &\times && 2 \\ \hline &&3&2 \\ \hline \end{array}

To multiply 32 by 2 we can use a vertical algorithm and multiply 2 by 2 to get 4 in the units column: \begin{array}{c} & & 3 &2 \\ &\times && 2 \\ \hline &&&4 \\ \hline \end{array}

Multiply 2 by 3 to get 6. We put this in the tens column: \begin{array}{c} & & 3 &2 \\ &\times && 2 \\ \hline &&6&4 \\ \hline \end{array}

The complete pattern is 8,\,16,\,32,\,64.

Idea summary

When we find a pattern with multiplying, we can use that to solve other multiplication problems.

### Outcomes

#### MA2-6NA

uses mental and informal written strategies for multiplication and division